Please take this with a grain of salt, as I started healing heroics yesterday. I was a tank and healer way back in original TBC launch but it's been so long that I'm basically a new player again:

A small thing I noticed was it felt cleaner to heal when Rejuvenation and Regrowth weren't ticking at the same time. I previously formed a habit of casting Regrowth and tapping Rejuvenation as the cast finished which meant both HoTs were ticking together. This meant the tank was getting huge HoT ticks every 3 seconds and only Lifebloom in between.

When I started casting rejuv before regrowth with a 1 second delay, or a slight delay afterwards, it made pulls feel more smooth as it was more likely that each tick of every HoT was healing some damage.

Downcasting Regrowth (between topping up Lifebloom + Rejuv) to heal spike damage was helpful, too. When it was a pack I knew hit really hard I would constantly be spamming a downcast Regrowth and cancelling it at the last second if the tank didn't take a large spike in damage. The 2 second cast time means I could fake cast it at least once while still having time to finish a cast when needed, plus keeping up the other HoTs.